# Answer to Question #10710 in Other Math for manthankhorwal

Question #10710

Simplify usinf identites:

186*186*186+14*14*14/186*186-186*14+14*14

186*186*186+14*14*14/186*186-186*14+14*14

Expert's answer

(186*186*186+14*14*14)/(186*186-186*14+14*14)

Let's recall that a3+b3=(a+b)(a2-ab+b2) . In the numerator we have sum of two cubes, in the denominator the second braces from the right part of mentioned formula. Therefore

(186*186*186+14*14*14)/(186*186-186*14+14*14)=(186+14)(186*186-186*14+14*14)/(186*186-186*14+14*14)= =186+14=200

Let's recall that a3+b3=(a+b)(a2-ab+b2) . In the numerator we have sum of two cubes, in the denominator the second braces from the right part of mentioned formula. Therefore

(186*186*186+14*14*14)/(186*186-186*14+14*14)=(186+14)(186*186-186*14+14*14)/(186*186-186*14+14*14)= =186+14=200

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